Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added Elements of Plane and Spherical TrigonometryCollins & Hannay, 1860 - 333 páginas |
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Página xiv
... proved . Indeed , those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
... proved . Indeed , those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
Página 132
... proved that the angle AGB is equal to the angle at F ; there fore the angle at F is greater than a right angle : But by the hypothe- sis , it is less than a right angle ; which is absurd , Therefore the an gles ABC , DEF are not unequal ...
... proved that the angle AGB is equal to the angle at F ; there fore the angle at F is greater than a right angle : But by the hypothe- sis , it is less than a right angle ; which is absurd , Therefore the an gles ABC , DEF are not unequal ...
Página 142
... proved , that similar figures of four sides , or of any number of sides , are one to another in the dupli- cate ratio of their homologous sides ; and the same has already been proved of triangles : therefore , universally similar ...
... proved , that similar figures of four sides , or of any number of sides , are one to another in the dupli- cate ratio of their homologous sides ; and the same has already been proved of triangles : therefore , universally similar ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore